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Compressed Sensing
This page contains resources about Compressed Sensing, Sparse Sampling and Sparse Signal Processing. Subfields and Concepts * Incoherence / Incoherent Sampling / Incoherent bases ** Canonical/Kroneker basis ** Fourier basis ** Random basis ** Random sequences / codes ** Inverse Discrete Cosine Transform (IDCT) / Heisenberg ** Wavelet basis * Coherent-based Sampling * Coherence / Mutual Coherence * Local Coherence * Null Space Property * Restricted Isometry Property * Underdetermined Linear System * Uncertainty Principles (between sparsity basis and measurement system) ** Continuous Uncertainty Principles (Heisenberg) ** Discrete Uncertainty Principle (Donoho and Stark) *** Dirac Comb / Picket Fence ** Quantitative Uncertainty Principle *** Quantitative Robust Uncertainty Principle * Sparse Approximation / Sparse Representation ** Basis Pursuit ** Matching Pursuit * Sparse Signal Recovery / Sparse Signal Reconstruction ** Exact Recovery Theorem ** Stable Recovery / Stability Theorem * Sub-Nyquist Sampling * Nonlinear Sampling Theorem * Iterative Reweighted Least Squares * Sparse Principal Component Analysis (PCA) * Structure Sparse PCA * B-Splines * E-Splines * Wavelets * Bayesian Compressive Sensing ** Variational Bayesian Compressive Sensing * Sparse Bayesian Models * Inverse Problems (Optimization) ** Regularization *** Regularized least squares *** L0 penalization / Spike-and-slab prior *** L1-regularization / LASSO / Laplace prior *** L2-regularization / Ridge Regression / Gaussian prior *** Elastic nets *** Total Variation (TV) Regularization (i.e. L1-norm of the gradient) Online Courses Video Lectures *Compressive Sensing and Sparse Recovery by Justin Romberg (Youtube ) Lecture Notes *Compressive sensing and Sparse optimization by Aswin C Sankaranarayanan *Compressed Sensing by Simon Foucart *Sparse Structure Recovery: Theory And Computation by Paul E. Hand *Compressed Sensing by Terence Tao *Computational Methods for Data Analysis by Nathan Kutz Books and Book Chapters *Theodoridis, S. (2015). "Chapter 9: Sparsity-Aware Learning". Machine Learning: A Bayesian and Optimization Perspective. Academic Press. *Hastie, T., Tibshirani, R., & Wainwright, M. (2015). "Chapter 10: Signal Approximation and Compressed Sensing". Statistical learning with sparsity: the lasso and generalizations. CRC Press. * Eldar, Y. C. (2015). Sampling theory: Beyond bandlimited systems. Cambridge University Press. *Carmi, A. Y., L. Mihaylova, & S. J. Godsill (Eds.). (2014). Compressed Sensing and Sparse Filtering. Springer. *Rish, I., & Grabarnik, G. (2014). Sparse modeling: theory, algorithms, and applications. CRC Press. *Foucart, S., & Rauhut, H. (2013). A mathematical introduction to compressive sensing. Birkhäuser. * Murphy, K. P. (2012). "Chapter 13: Sparse linear models". Machine Learning: A Probabilistic Perspective. MIT Press. * Baraniuk, R., Davenport, M. A., Duarte, M. F., & Hegde, C. (2011). An introduction to compressive sensing. Connexions e-textbook. * Starck, J. L., Murtagh, F., & Fadili, J. M. (2010). "Chapter 11: Compressed Sensing". Sparse image and signal processing: wavelets, curvelets, morphological diversity. Cambridge University Press. * Elad, M. (2010). Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer. * Mallat, S. (2008). A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press. * Saad, Y. (2003). Iterative Methods for Sparse Linear Systems. Siam. *MacKay, D. J. (2003). "Part VI: Sparse Graph Codes". Information Theory, Inference and Learning Algorithms. Cambridge University Press. Scholarly Articles * Chen, Y., Bhojanapalli, S., Sanghavi, S., & Ward, R. (2014). Coherent matrix completion. In Proceedings of the 31st International Conference on Machine Learning (pp. 674-682). * Davenport, M. A., Duarte, M. F., Eldar, Y. C., & Kutyniok, G. (2011). Introduction to compressed sensing. Preprint, 93(1), 2. * Fornasier, M., & Rauhut, H. (2011). Compressive sensing. In Handbook of mathematical methods in imaging (pp. 187-228). Springer New York. * Yang, J., Wright, J., Huang, T. S., & Ma, Y. (2010). Image super-resolution via sparse representation. IEEE Transactions on image processing, 19(11), 2861-2873. * Dai, W., & Milenkovic, O. (2009). Subspace pursuit for compressive sensing signal reconstruction. IEEE Transactions on Information Theory, 55(5), 2230-2249. * Starck, J. L., & Fadili, M. J. (2009). An overview of inverse problem regularization using sparsity. In Image Processing (ICIP), 16th IEEE International Conference on, 1453-1456. * Duarte, M. F., Davenport, M. A., Takhar, D., Laska, J. N., Sun, T., Kelly, K. E., & Baraniuk, R. G. (2008). Single-pixel imaging via compressive sampling.IEEE Signal Processing Magazine, 25(2), 83. * Ji, S., Xue, Y., & Carin, L. (2008). Bayesian compressive sensing. IEEE Transactions on Signal Processing, 56(6), 2346-2356. * Candès, E. J., & Wakin, M. B. (2008). An introduction to compressive sampling. IEEE Signal Processing Magazine, 25(2), 21-30. * Blu, T., Dragotti, P. L., Vetterli, M., Marziliano, P., & Coulot, L. (2008). Sparse sampling of signal innovations. IEEE Signal Processing Magazine, 25(2), 31-40. * Lustig, M., Donoho, D. L., Santos, J. M., & Pauly, J. M. (2008). Compressed sensing MRI. IEEE Signal Processing Magazine, 25(2), 72-82. * Lustig, M., Donoho, D., & Pauly, J. M. (2007). Sparse MRI: The application of compressed sensing for rapid MR imaging. Magnetic resonance in medicine, 58(6), 1182-1195. * Dragotti, P. L., Vetterli, M., & Blu, T. (2007). Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strang–Fix.IEEE Transactions on Signal Processing, 55(5), 1741-1757. * Baraniuk, R. G. (2007). Compressive sensing. IEEE Signal Processing Magazine, 24(4). * Candes, E., & Romberg, J. (2007). Sparsity and incoherence in compressive sampling. Inverse problems, 23(3), 969. * Candes, E. J., Romberg, J., & Tao, T. (2006). Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information.IEEE Transactions on information theory, 52(2), 489-509. * Candes, E. J., Romberg, J. K., & Tao, T. (2006). Stable signal recovery from incomplete and inaccurate measurements. Communications on pure and applied mathematics, 59(8), 1207-1223. * Candse, E. J. (2006, August). Compressive sampling. In Proceedings of the international congress of mathematicians (Vol. 3, pp. 1433-1452). * Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on information theory, 52(4), 1289-1306. * Castro, R., Haupt, J., & Nowak, R. (2006). Compressed sensing vs. active learning. In IEEE International Conference on Acoustics, Speech and Signal Processing, Proceedings. (Vol. 3, pp. III-III). IEEE. * Elad, M., & Bruckstein, A. M. (2002). A generalized uncertainty principle and sparse representation in pairs of bases. IEEE Transactions on Information Theory, 48(9), 2558-2567. * Donoho, D. L., & Stark, P. B. (1989). Uncertainty principles and signal recovery. SIAM Journal on Applied Mathematics, 49(3), 906-931. Tutorials * Sparse Signal Processing by Pier Luigi Dragotti (Part 1) - 2015 * Sparse Signal Processing by Pier Luigi Dragotti (Part 2) - 2015 * Tradeoffs between Speed and Accuracy in Inverse Problems by Raja Giryes Software *pycompsense - Python *pyCSalgos - Python *Sparco - MATLAB *SparseLab - MATLAB *SparseMRI - MATLAB *SPArse Modeling Software (SPAMS) - Python and R *KL1p - C++ See also *Optimization * Information Theory *Dimensionality Reduction (e.g. PCA) *Sparse Coding *Statistical Signal Processing *Digital Signal Processing *Digital Image Processing *Probability Theory Other Resources * Learning Compressed Sensing - Nuit Blanche blog * Compressive Sensing - Reddit * Compressive Sensing on Google+ - online community * Compressive Sensing Resources - Rice * Compressive Sensing: The Big Picture * Compressive Sensing:A New Framework for Imaging * Uncertainty Principle in Quantum Physics and Signal Processing - blog post * A Brief Introduction to Compressed Sensing with Scikit-Learn - blog post * Compressive sensing: tomography reconstruction with L1 prior (Lasso) - blog post * Compressed Sensing in Python - blog post * Image reconstruction using compressed sensing - StackExchange Category:Signal Processing Category:Optimization Category:Information Theory